Answer :
To solve the equation [tex]\(4x^2 - 3 = 1\)[/tex], we need to isolate [tex]\(x^2\)[/tex] first:
1. Start with the given equation:
[tex]\[ 4x^2 - 3 = 1 \][/tex]
2. Add 3 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 4x^2 - 3 + 3 = 1 + 3 \][/tex]
[tex]\[ 4x^2 = 4 \][/tex]
3. Divide both sides by 4 to solve for [tex]\(x^2\)[/tex]:
[tex]\[ \frac{4x^2}{4} = \frac{4}{4} \][/tex]
[tex]\[ x^2 = 1 \][/tex]
4. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \pm1 \][/tex]
So, the possible values for [tex]\(x\)[/tex] are 1 and -1.
Next, we need to determine the value of [tex]\(1 - 2\)[/tex] for each solution of [tex]\(x\)[/tex]:
5. For [tex]\(x = 1\)[/tex]:
[tex]\[ 1 - 2 = -1 \][/tex]
6. For [tex]\(x = -1\)[/tex]:
[tex]\[ -1 - 2 = -3 \][/tex]
Thus, the values of [tex]\(1 - 2\)[/tex], given the solutions to the equation, are -1 and -3. Hence, the right answer among the given options for a value of [tex]\(1 - 2\)[/tex] corresponding to the computed [tex]\(x\)[/tex] values is:
[tex]\[ (a) -1 \][/tex]
So the correct choice is:
[tex]\[ (a) -1 \][/tex]
1. Start with the given equation:
[tex]\[ 4x^2 - 3 = 1 \][/tex]
2. Add 3 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 4x^2 - 3 + 3 = 1 + 3 \][/tex]
[tex]\[ 4x^2 = 4 \][/tex]
3. Divide both sides by 4 to solve for [tex]\(x^2\)[/tex]:
[tex]\[ \frac{4x^2}{4} = \frac{4}{4} \][/tex]
[tex]\[ x^2 = 1 \][/tex]
4. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \pm1 \][/tex]
So, the possible values for [tex]\(x\)[/tex] are 1 and -1.
Next, we need to determine the value of [tex]\(1 - 2\)[/tex] for each solution of [tex]\(x\)[/tex]:
5. For [tex]\(x = 1\)[/tex]:
[tex]\[ 1 - 2 = -1 \][/tex]
6. For [tex]\(x = -1\)[/tex]:
[tex]\[ -1 - 2 = -3 \][/tex]
Thus, the values of [tex]\(1 - 2\)[/tex], given the solutions to the equation, are -1 and -3. Hence, the right answer among the given options for a value of [tex]\(1 - 2\)[/tex] corresponding to the computed [tex]\(x\)[/tex] values is:
[tex]\[ (a) -1 \][/tex]
So the correct choice is:
[tex]\[ (a) -1 \][/tex]
